Problem: $ \left(\dfrac{27}{8}\right)^{-\frac{2}{3}}$
Explanation: $= \left(\dfrac{8}{27}\right)^{\frac{2}{3}}$ $= \left(\left(\dfrac{8}{27}\right)^{\frac{1}{3}}\right)^{2}$ To simplify $\left(\dfrac{8}{27}\right)^{\frac{1}{3}}$ , figure out what goes in the blank: $\left(? \right)^{3}=\dfrac{8}{27}$ To simplify $\left(\dfrac{8}{27}\right)^{\frac{1}{3}}$ , figure out what goes in the blank: $\left({\dfrac{2}{3}}\right)^{3}=\dfrac{8}{27}$ so $ \left(\dfrac{8}{27}\right)^{\frac{1}{3}}=\dfrac{2}{3}$ So $\left(\dfrac{8}{27}\right)^{\frac{2}{3}}=\left(\left(\dfrac{8}{27}\right)^{\frac{1}{3}}\right)^{2}=\left(\dfrac{2}{3}\right)^{2}$ $= \left(\dfrac{2}{3}\right)\cdot\left(\dfrac{2}{3}\right)$ $= \dfrac{4}{9}$